Answer to Question #305357 in Statistics and Probability for Adrian

Question

Suppose three coins are tossed. Let Y be the random variable representing the number of tails that occur. Find the values of the random variable Y

Answer 1

Let's denote $H$ - heads, $T$ - tails.

There are $2^3=8$ possible outcomes

$S=\{HHH, HHT, HTH, THH,$

$HTT, THT, TTH, TTT\}$

The possible values of the random variable $Y$ are $0, 1, 2, 3.$

$\def\arraystretch{1.5} \begin{array}{c:c} Possible \ Outcomes & Y \\ \hline HHH & 0\\ \hdashline HHT & 1 \\ \hdashline HTH & 1 \\ \hdashline THH & 1 \\ \hdashline HTT & 2 \\ \hdashline THT & 2 \\ \hdashline TTH & 2 \\ \hdashline TTT & 3 \\ \hdashline \end{array}$

We will assume that the probability of getting heads and tails is the same:

$p = q =1/2$

Construct the probability distribution of the random variable

$\def\arraystretch{1.5} \begin{array}{c:c} y & 0 & 1 & 2 & 3 \\ \hline p(y) & 1/8 & 3/8 & 3/8 & 1/8 \end{array}$

or

$\def\arraystretch{1.5} \begin{array}{c:c} y & 0 & 1 & 2 & 3 \\ \hline p(y) & 0.125 & 0.375 & 0.375 & 0.125 \end{array}$